Uniqueness of meromorphic functions that share Two Sets

In this note, we present one uniqueness theorem which shows how two meromorphic functions are uniquely determined by their two finite shared sets. These sharing sets are a new kind of pair of finite range sets in $\mathbb{C}$ for meromorphic functions corresponding to their uniqueness. Moreover, we answered a question positively raised in (\cite{1}).Comment: 9 page

A Study on Solute Dispersion in a Three Layer Blood-like Liquid Flowing through a Rigid Artery

The unsteady dispersion of a solute has been discussed by the method of generalized dispersion technique in a blood-like liquid flowing through a pipe under the combined effects of finite yield stress and irreversible absorption into the wall.The solvent is enacted as a three-layered liquid by considering the center liquid as a Casson liquid (a core of red blood cell suspension) and a peripheral layer of plasma as a Newtonian liquid. An asymptotic representation for the convection and dispersion coefficients has been shown only for large values of time, which will not hamper the study of physical behavior of the system. The objective of the present study is to examine the nature of exchange coefficient, convective coefficient and in particular, dispersion coefficient together with mean concentration distribution under the effect of absorption parameter (​β)​, yield stress (​​τ​y​​​) (equivalently the plug radius (​​Rp​​​)) and peripheral layer variation (i.e., ratio of central core radius to normal artery radius (​​Ro​​​)). It is found that the presence of peripheral layer makes some important increment in dispersion coefficient compared to single phase Casson liquid for small absorption. Increase in both diffusivity (D*​​) and Peclet number (Pe) make a significant decrement in the magnitude of dispersion coefficient with respect to absorption rate. The decrease in peak of the mean concentration distribution with the increase in reaction rate is found irrespective of the nature of reaction